I am understanding that the Hydrogen ions oxidize the calcium metal, neutralizing itself and creating a calcium cation. My question is why does the Hydrogen oxidize the calcium? Doesn't it prefer to have an empty outer shell? Does it want more to be neutral or to have an empty outer shell?
This is a simple example of the reactivity series. More reactive metals will displace less reactive metal ions, and they switch places, with the more reactive metal becoming the ion and and the less reactive ion becoming a metal. This can be very cool in many situations: for example, copper metal can displace a silver salt to plate silver metal and produce a blue copper salt. See this video! In any case, hydrogen is consider a reference "metal" in the reactivity series, and it is less reactive than calcium, so the displacement reaction you cite occurs.